> [To recap, we have a machine and operator in Australia and another
> machine and operator in Vienna. The question is whether the Viennese
> machine can continue the computation of the Australian machine, and
> whether any associated consciousness also continues without
> interruption. S(n) is the last state of the Australian machine which
> the Australian operator notes and passes on, either explicitly or
> hidden in false data, to his Viennese counterpart, who then endeavours
> to calculate or look up the next state S(n+1) to input into his
> machine.]

Excellent summary.

>> I see. In other words, it's as though the Vienna operator, a
>> very smart dude, works out *himself* with, say, his pocket
>> calculator, S(n+1). Quite all right with me. I don't think it
>> ever matters where a computation is done, nor on what
>> hardware. Just so that it's a real computation, and so
>> sustains real causality and information flow.
>
> And you will hopefully allow that in this step, working out the next
> state could involve a lookup table. This low level lookup simply
> mimics the physics of the machine, and is not like looking up the
> answer to a computation in order to bypass all the intermediate steps.

Yes. The lower the level of the lookup table in a computation apparently
isomorphic to a conscious being, the more consciousness is retained.
Looking up very small patches in Conway's Life (i.e., just as a crude
guess, patches less than 100x100) has utterly no effect on consciousness.

>> > i.e. the same as if the Vienna operator knew nothing about the
>> > antipodean device and simply tried random states, one of them just
>> > happening to be S(n+1). How does this affect whether consciousness is
>> > interrupted?
>>
>> Very good question. In that case there is an infinitesimal interruption in
>> consciousness, because there was no genuine information flow or
>> causality, in other words, to me, not a real computation at all. All
>> possible things are tried in Vienna. I think I see where you are going,
>> but I'll let you deliver the next blow! :-)
>
> Would it make a difference if the Viennese operator worked out the
> appropriate state? Here are several possibilities:
>
> (a) The file I've received says that the final state of the Australian
> machine was S-6754. The successor state for that is S-2037, so if I
> input that into my machine, the computation won't know it has been
> spread across two continents.

How did you get a hold of S-2037? If you looked it up somewhere,
or heard from a little bird that you should try S-2037, then the answer
would be no. But if you worked out, i.e., your brain emulated the
machine itself, i.e. calculated state S-2037 from S-6754, then yes,
no infinitesiaml interruption occurred. (And just for the record, no tiny
interruptions in consciousness matter much to me. They have to be
significantly many, consecutive or not, over some given period of time.)

> (b) The file I've received gives the final state of the Australian
> machine as either S-6754 or S-789. Their respective successor states
> are S-2037 and S-9175, so I'll try both of those, and when I get the
> right one, the computation and its consciousness will have been
> implemented without interruption.

Yes. The other run will either occur entirely incorrectly, or, after
somehow getting back on track, will suffer even more than that
tiny interruption of consciousness.

> (c) The file from Australia lists all possible machine states S-1 to
> S-9999. I have a lot of work ahead of me, but one of them has to be
> the right one. First, I'll input S-1, the successor state of S-3412;
> then S-2, which as everyone knows is the successor state of S-439;
> next, S-3, successor of S-2031 (or was it S-3021? I always get those
> two mixed up but it's definitely one or the other)... and so on to
> S-9999.

Yes. Unless I've missed something, I think that this is just the
logical next step after (b), and so the answer is should be just
the same. All of these here in (c) seem to me to implement a
computation that has one non-causal step, i.e., a tiny tiny
lapse of consciousness.

> You can see that the Vienna operator's muttering as he goes about his
> work in the last example has no effect on the mechanics of the
> computation. As he inputs S-2037 he could be thinking that it is the
> successor of S-6754, or he could be thinking about what he will have
> for dinner, and it will make no difference to his behaviour as he is
> just inputting all the states anyway.
>
> In which of the above cases is the causal link between the two
> machines preserved? In which does consciousness continue
> uninterrupted?

I believe that I have answered. In some cases, the state S-2037
really was computed in a local calculation, and in some cases it
was gotten by chance, more or less. In the former there were no
interruptions of consciousness, but in the latter there were.